For our last experiment, we study the recovery of PDEs under substantial measurement noise. This is likely the regime most relevant to advancing modern science and engineering practice. In particular, we study the one-dimensional Kuramoto-Sivashinsky equation [1]}, an early model of laminar flame fronts, and the two-dimensional reaction diffusion system, a ubiquitous model in chemistry. The Kuramoto-Sivashinsky in spatial dimension \(x\)  and time \(t\)  is given by
\(u_t = -uu_x - u_{xx} - u_{xxxx}\) 
